Which of the following values for m makes the inequality m−−√+17

Question

Which of the following values for m makes the inequality  m−−√+17<24
  true?(1 point)
Responses

64
64

50
50

49
49

48
48
Rema

GPT-4o mini · Answer

To solve the inequality $\sqrt{m} + 17 < 24$, we can start by isolating the square root: 1. Subtract 17 from both sides: $$ \sqrt{m} < 24 - 17 $$ $$ \sqrt{m} < 7 $$ 2. Square both sides to eliminate the square root: $$ m < 7^2 $$ $$ m < 49 $$ Now we need to check which of the given values for $m$ satisfies this inequality: - For $m = 64$: $64 < 49$ is **false**. - For $m = 50$: $50 < 49$ is **false**. - For $m = 49$: $49 < 49$ is **false**. - For $m = 48$: $48 < 49$ is **true**. Thus, the value of $m$ that makes the inequality true is **48**.